Whisk together soy sauce, water, rice wine, white sugar, brown sugar, garlic, ginger, and cornstarch in a multi-functional pressure cooker (such as Instant Pot). Add carrots and toss to coat.
Close and lock the lid. Turn on Instant Pot and select high pressure according to manufacturer's instructions. Set timer for 2 minutes. Allow about 10 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Serve carrots sprinkled with toasted sesame seeds.